Common Properties

• Window is a rectangular window plus a scaled cosine, where the cosine has one period across the window.
• Symmetric ( zero or linear phase)
• Positive (by convention on and )
• Main lobe is radians per sample wide, where .
• Zero-crossings (``notches'') in window transform at intervals of outside of main lobe.

Figure 3.6 compares the window transforms for the rectangular, Hann, and Hamming windows. Note how the Hann window has the fastest roll-off while the Hamming window is closest to being equal-ripple. The rectangular window has the narrowest main lobe.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.